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rhodes (ajr2283) – HW08 – Gilbert – (56380)
1
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001
10.0 points
Which, iF any, oF the Following
A.
−
−−→
QP ,
B.
PQ,
are representations oF vectors when
P, Q
are
points in 3space?
1.
both oF them
2.
A only
correct
3.
neither oF them
4.
B only
Explanation:
A. TRUE:
−
−−→
QP
is the displacement vector
having initial point
P
and terminal point
Q
.
B. ±ALSE:
PQ
is the line segment from
P
to
Q
.
keywords: vectors, scalars, T/±, line segment,
displacement vector, length
002
10.0 points
±ind the vector
v
having a representation
by the directed line segment
−−→
AB
with respect
to points
A
(3
,
−
2) and
B
(
−
2
,
1).
1. v
=
a−
1
,
−
1
A
2. v
=
a−
5
,
−
3
A
3. v
=
a
5
,
3
A
4. v
=
a−
5
,
3
A
correct
5. v
=
a
1
,
−
1
A
6. v
=
a
1
,
1
A
Explanation:
Since
−−→
AB
=
a−
2
−
3
,
1 + 2
A
,
we see that
v
=
a−
5
,
3
A
.
003
10.0 points
When
u
,
v
are the displacement vectors
u
=
−→
AP ,
v
=
−→
AC ,
determined by the parallelogram
A
B
C
P
Q
R
S
O
express
−−→
QC
in terms oF
u
and
v
.
1.
−−→
QC
=
1
2
u
+
v
2.
−−→
QC
=
1
2
u
−
v
3.
−−→
QC
=
u
+
1
2
v
4.
−−→
QC
=
−
1
2
v
5.
−−→
QC
=
−
1
2
u
6.
−−→
QC
=
1
2
v
−
u correct
Explanation:
By the parallelogram law For the addition
oF vectors we see that
−−→
QC
=
1
2
v
−
u
.
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View Full Documentrhodes (ajr2283) – HW08 – Gilbert – (56380)
2
004
10.0 points
Determine
a
so that the vector
u
=
a−
11
,
−
4
A
is a linear combination
u
=
a
v
+
b
w
of vectors
v
=
a
3
,
1
A
,
w
=
a
2
,
1
A
.
1.
a
= 2
2.
a
=
−
3
correct
3.
a
=
−
2
4.
a
=
−
1
5.
a
= 3
Explanation:
Since addition and scalar multiplication of
vectors is carried out componentwise, we see
that
u
=
a−
11
,
−
4
A
=
a
a
3
,
1
A
+
b
a
2
,
1
A
=
a
3
a
+ 2
b, a
+
b
A
.
Thus
3
a
+ 2
b
=
−
11
,
a
+
b
=
−
4
.
Consequently, after solving these for
a
we see
that
a
=
−
3
.
keywords: vectors, vector sum, linear combi
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 Spring '07
 TextbookAnswers
 Multivariable Calculus

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